Tim Cook and Jony Ive discuss the synergy between Apple and fashion, two worlds fueled by curiosity and change.

For much of the last year, a pyramid of dug-up earth has loomed over the 175-acre Northern California park where Apple’s future headquarters, a vast ring designed by Norman Foster, is rising out of glass and steel.

“Hard to know which is more beautiful, the building or that pile of dirt,” says Apple CEO Tim Cook with a wide smile on a recent morning, as he stands among the construction crew in their acid-yellow vests and gazes at the tall mountain of soil, its stepped surfaces painted a dark gold by the sun. Not a speck of dirt is to be removed from the campus; instead it will nourish a forest of more than 7,000 trees, which in turn will nourish a village of some 13,000 techies tinkering in silicon. In its current form, the pyramid suggests nothing so much as Giza brought to Cupertino, as if that ancient triumph of human hands had decided to seek an audience with the high priests of technology.

From aerial mock-ups, the building variously suggests a spaceship that has touched down gently in a clearing or a softened, highly styled Pentagon, sure to contain as many secrets. The $5 billion, 2.8 million–square foot structure was originally commissioned by Steve Jobs in 2009, in what Foster describes as “a series of rather amusing phone conversations.” Jobs waxed nostalgic about growing up amid the citrus groves of Northern California and wandering through the outdoor corridors of Stanford as an undergraduate. He took the architect to the cathedral-like building on the Pixar campus north of Oakland, which Jobs designed himself with the goal of keeping everyone and everything under one roof.

The $5 billion, 2.8 million–square foot circular headquarters was originally commissioned by Steve Jobs in 2009, in what architect Norman Foster describes as “a series of rather amusing phone conversations.”

“There was from the outset a concern with breaking down barriers,” says Foster—the circular form is intended to encourage chance encounters outside the corporate box. Foster’s vision includes nearly four miles of curved glass and will be powered by one of the world’s largest solar-paneling grids. “The sheets of glass are so long, so clear, that you don’t feel that there is a wall between you and the landscape,” he says. “And at the same time the building is an echo of the ethos of Apple, which designs artifacts that, though they fulfill all sorts of functions, exist abstractly in their own right.” Scheduled for completion later this year, it is both Apple’s flagship and an Apple product par excellence—a sleek container worthy of the sophisticated machinery within. “In what we do,” observes Cook, “design is crucial, as it is in fashion.”

Apple’s lexicon of pure, pared-down forms, smooth surfaces, gleaming metallic colors, and soft contours within hard carapaces has emerged over the past 20 years under the eye of chief designer Jony Ive. Talking over coffee on the old campus about the growing synergy between the company and the fashion world, Ive points to his rose-gold Apple Watch, a precious counterpoint to the Clarks on his feet. “Nine years ago, the iPhone didn’t exist, and the most personal product we had was too big to carry around with you,” he explains. “The technology is at last starting to enable something that was the dream of the company from the very beginning—to make technology personal. So personal that you can wear it.”

In the fall of 2014, Apple held an event at Colette, the Paris boutique, to introduce the Apple Watch to the fashion crowd. The following year, for the first time in its 40-year history, Apple invited a fashion house to collaborate on the design of a product: the Apple Watch Hermès, a square of highly intelligent steel fixed to a hand-stitched leather strap. “That watch,” says Ive, “is the result of two temperamentally, philosophically aligned companies’ deciding to make something together.”

Tom Ford, who used to outlaw cell phones at his fashion shows, released a video in lieu of a runway show last October. He imagined his admirers turning their iPhones sideways to watch Lady Gaga perform on behalf of his spring collection. Now, says Ford, “I view Apple products as fashion accessories.” Like other houses, such as Saint Laurent and Lanvin, he designs with these products in mind. “I even created silver and gold pocket chains for the Apple Watch,” he says.

This May, the Metropolitan Museum of Art’s Costume Institute will explore the relationship between fashion and technology in the exhibition “Manus x Machina.” Apple is the show’s sponsor, and Ive is a cochair of the opening-night gala. For a company that has long been engaged in the project of dissolving the old tension between man and machine, it’s a pairing made in collaboration heaven.

“Both the hand and the machine can produce things with exquisite care or with no care at all,” says Ive. “But it’s important to remember that what was seen at one time as the most sophisticated technology eventually becomes tradition. There was a time when even the metal needle would have been seen as shocking and profoundly new.”